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Social Choice and Welfare

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26.10.2020 | Original Paper

Social Capital, Communication Channels and Opinion Formation

verfasst von: Christos Mavridis, Nikolas Tsakas

Erschienen in: Social Choice and Welfare | Ausgabe 4/2021

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Abstract

We study how different forms of social capital lead to different distributions of multidimensional opinions by affecting the channels through which individuals communicate. We develop a model to compare and contrast the evolution of opinions between societies whose members communicate through bonding associations (i.e., which bond similar people together) and societies where communication is through bridging associations (i.e., which bridge the gap among different people). Both processes converge towards opinion distributions where there are groups within which there is consensus in all issues. Bridging processes are more likely to lead to society-wide consensus and converge to distributions that have, on average, fewer opinion groups. The latter result holds even when the confidence bound that allows successful communication in the bridging process is much smaller than the respective bound in the bonding process.

Vorheriger Artikel Stabbed in the back? Mandated political representation and murders

Nächster Artikel Fairness views and political preferences: evidence from a large and heterogeneous sample

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This is in fact a recurrent result in this type of processes, see Deffuant et al. (2000) and Lorenz (2005).

See Bala and Goyal (1998); Gale and Kariv (2003); Banerjee and Fudenberg (2004); Acemoglu and Ozdaglar (2011); DeMarzo et al. (2003); Golub and Jackson (2010); Mueller-Frank (2013,2015) and also Golub and Sadler (2017) for an excellent review of the different branches of literature on learning on networks.

For other definitions of social capital and for a research survey on the topic see Durlauf and Fafchamps (2005). For an empirical decomposition of the concept see Bjørnskov (2006).

There are also two forms of “bridging”, internal and external. Internal bridging brings together the members of a given association, whereas external bridging brings together members of different associations (see Geys and Murdoch 2008). Moreover, Geys and Murdoch (2010) discuss how the bridging and bonding nature of networks can be measured. Following the discussion on social capital and redistribution, Borisova et al. (2015) show that it is in fact the bridging social capital that has positive effects on redistribution.

For an excellent survey on opinion dynamics and bounded confidence see Lorenz (2007) and for some empirical evidence see Lorenz (2017). Moreover, a stream of the literature on average-based updating looks at the shape of persisting disagreement without considering bounded confidence (see DeMarzo et al. 2003; Louis et al. 2017).

EVS (2011): European Values Study 2008: Integrated Dataset (EVS 2008). GESIS Data Archive, Cologne. ZA4800 Data file Version 3.0.0, doi:10.4232/1.11004

We focus on the variable that indicates whether or not someone has provided voluntary work for the given organization, rather than just having participated, as this provides a stronger indication on the extent of involvement in the organization.

The choice of twenty observations as a threshold is obviously ad hoc, as there is not standard way of making this choice. The idea is that on the one hand a small number of observations induces a lot of noise in the ELF, on the other hand setting a high threshold will lead us to drop too many observations, thus altering the nature of the total sample.

The complete table of regression results is available upon request.

In a different set of regressions we found the same result to be true if one looks at partisanship levels instead of the ELF. By partisanship level we mean the average absolute distance from the average opinion of 5.5. This result could be connected with the findings of Satyanath et al. (2017) where the authors find participation in associations to be linked with increased entry level in the Nazi party before WWII.

Alternatively, one could think that two citizens with very distant opinions can never be chosen to interact. The qualitative results of this alternative mechanism are identical and the only feature that is affected is the speed of convergence and some increased consistency of extreme opinions.

There might be cases where these two opinions might be ex-ante correlated, but this would not add anything to our model.

Later in the paper, for some results we will impose the normalization \(k=\frac{1}{2}-\sqrt{\frac{1}{4}-d^2}\) which ensures that the areas within which successful communication is possible cover the same area in each case. Observing at Fig. 1 the area in which a citizen may find others to agree is \(4d^2\) in the bonding case and \(2\cdot 2k-4k^2\) in the bridging case. Equating the two quantities yields the normalized value of the parameter k.

We consider that the citizens discuss a single issue at a time, however all results directly extend to the case in which both issues are discussed simultaneously. Such an assumption would only speed up the convergence of the process.

The proofs of these arguments are omitted as they are rather straightforward and well–established in the literature and are available upon request.

A short discussion on why focusing on the interior of the neighboring area is provided in the Appendix after the proof of the proposition.

The proof is readily available upon request.

The choices regarding the confidence bounds are made in order to have a unique expression for the probabilities we calculate. Our analysis allows us to calculate the respective probabilities for larger values as well, but that would induce a larger computational cost without adding much to the intuition. The assumption regarding successful communication does not affect the result; it just eliminates all interactions that lead to no update which affect only the speed of convergence.

A simple Taylor expansion gives \(\frac{1}{2}-\sqrt{\frac{1}{4}-d^2}=d^2+d^4+2d^6+5d^8+O[d^{10}]\).

We use as conditions for stabilization those of Propositions 2 and 3, which are sufficient for us to count the number of islands, as explained in Remark 3.

As a reminder, \(ELF=1-\sum s_i^2\) and \(GI=\sum \sum s_i s_j d_{ij}\), where \(s_i\) and \(s_j\) are shares of distinct opinion islands, and \(d_{ij}\) is the Euclidean distance between opinion islands i and j.

Lorenz (2005) states the result focusing on the limit of the backward product of transition matrices, which is equivalent to the consensus argument we present here.

Otherwise, if at least two of the citizens are sufficiently close to interact successfully, this will be true in all subsequent periods and hence by Proposition 1 there will be at most two islands in the long run.

In order to have two or fewer islands, at least two citizens must have exactly the same initial opinions, which has probability zero of occurring given the assumed distribution initial opinions are drawn from.

Acemoglu D, Como G, Fagnani F, Ozdaglar A (2013) Opinion fluctuations and disagreement in social networks. Math Oper Res 38(1):1–27CrossRef

Acemoglu D, Ozdaglar A (2011) Opinion dynamics and learning in social networks. Dyn Games Appl 1:3–49CrossRef

Axelrod R (1997) The dissemination of culture. A model with local convergence and global polarization. J Conflict Resolut 41(2):203–226CrossRef

Bala V, Goyal S (1998) Learning from neighbors. Rev Econ Stud 65(3):595–621CrossRef

Banerjee A, Fudenberg D (2004) Word-of-mouth learning. Games Econ Behav 46(1):1–22CrossRef

Ben-Naim E, Krapivsky PL, Redner S (2003) Bifurcations and patterns in compromise processes. Phys D 183(3–4):190–204CrossRef

Bjørnskov C (2006) The multiple facets of social capital. Eur J Polit Econ 22:22–40CrossRef

Blondel VD, Hendrickx JM, Tsitsiklis JN (2007) On the 2r conjecture for multi-agent systems. In: 2007 European Control Conference (ECC), Kos, pp 874–881

Borisova E, Govorun A, Ivanov D (2015) Bridging or bonding? Preferences for redistribution and social capital in Russia, Mimeo

Coffé H, Geys B (2008) Measuring the bridging nature of voluntary organizations: the importance of association size. Sociology 42(2):357–369CrossRef

Dandekar P, Goel A, Lee DT (2013) Biased assimilation, homophily, and the dynamics of polarization. Proc Nat Acad Sci 110(15):5791–5796CrossRef

Deffuant G, Neau D, Amblard F, Weisbuch G (2000) Mixing beliefs among interacting agents. Adv Complex Syst 03(01n04):87–98CrossRef

DeGroot MH (1974) Reaching a consensus. J Am Stat Assoc 69(345):118–121CrossRef

DeMarzo PM, Vayanos D, Zwiebel J (2003) Persuasion bias, social influence, and uni-dimensional opinions. Q J Econ 118(3):909–968CrossRef

Durlauf SN, Fafchamps M (2005) Social capital. In: Aghion P, Durlauf SN (eds) Handbook of economic growth, vol 1. Part B. Elsevier, Amsterdam, pp 1639–1699

Fortunato S, Latora V, Pluchino A, Rapisarda A (2005) Vector opinion dynamics in a bounded confidence consensus model. Int J Mod Phys C 16(10):1535–1551CrossRef

Friedkin NE, Johnsen EC (1990) Social influence and opinions. J Math Sociol 15(3–4):193–206CrossRef

Gale D, Kariv S (2003) Bayesian learning in social networks. Games Econ Behav 45(2):329–346CrossRef

Geys B, Murdoch Z (2008) How to make head or tail of ‘bridging’ and ‘bonding’?: addressing the methodological ambiguity. Br J Sociol 59(3):435–454CrossRef

Geys B, Murdoch Z (2010) Measuring the ‘bridging’ versus ‘bonding’ nature of social networks: a proposal for integrating existing measures. Sociology 44(3):523–540CrossRef

Golub B, Jackson MO (2010) Naïve learning in social networks and the wisdom of crowds. Am Econ J Microecon 2(1):112–149CrossRef

Golub B, Jackson MO (2012) How homophily affects the speed of learning and best-response dynamics. Q J Econ 127(3):1287–1338CrossRef

Golub B, Sadler E (2017) Learning in social networks. In: Yann B, Galeotti A, Rogers B (eds) Oxford handbook of the economics of networks. Oxford University Press, Oxford

Granovetter MS (1973) The strength of weak ties. Am J Sociol 78(6):1360–1380CrossRef

Guiso L, Sapienza P, Zingales L (2004) The role of social capital in financial development. Am Econ Rev 94(3):526–556CrossRef

Hegselmann R, Krause U (2002) Opinion dynamics and bounded confidence models, analysis and simulation. J Artif Soc Soc Simul 5(3)

Holme P, Newman ME (2006) Nonequilibrium phase transition in the coevolution of networks and opinions. Phys Rev E 74(5):056108CrossRef

Iijima R, Kamada Y (2017) Social distance and network structures. Theor Econ 12(2):655–689CrossRef

Knack S, Keefer P (1997) Does social capital have an economic pay-off? A cross-country investigation. Q J Econ 112(4):1251–1288CrossRef

Krause U (2000) A discrete nonlinear and non-autonomous model of consensus formation. In: Elaydi S, Ladas G, Popenda J, Rakowski J (eds) Communications in difference equations. Gordon and Breach Publ, Amsterdam, pp 227–236

Kurahashi-Nakamura T, Mäs M, Lorenz J (2016) Robust clustering in generalized bounded confidence models. J Artif Soc Soc Simul 19(4):7CrossRef

Lorenz J (2003) Multidimensional opinion dynamics when confidence changes. In: Economic Complexity 2003, Aix-en-Provence, France

Lorenz J (2005) A stabilization theorem for dynamics of continuous opinions. Phys A 355(1):217–223CrossRef

Lorenz J (2007) Continuous opinion dynamics under bounded confidence: a survey. Int J Mod Phys C 18(12):1819–1838CrossRef

Lorenz J (2008) Fostering consensus in multidimensional continuous opinion dynamics under bounded confidence. In: Helbing D (ed) Managing complexity: insights, concepts, applications. Springer, Berlin, pp 321–334CrossRef

Lorenz J (2017) Modeling the evolution of ideological landscapes through opinion dynamics. In: Jager W, Verbrugge R, Flache A, de Roo G, Hoogduin L, Hemelrijk C (eds) Advances in social simulation 2015. Springer, Cham, pp 255–266CrossRef

Louis P, Troumpounis O, Tsakas N (2017) Communication and the emergence of a unidimensional world. In: SSRN working paper

Melguizo I (2018) Homophily and the persistence of disagreement. Econ J 129(619):1400–1424CrossRef

Mueller-Frank M (2013) A general framework for rational learning in social networks. Theor Econ 8(1):1–40CrossRef

Mueller-Frank M (2015) Reaching consensus in social networks. In: SSRN working paper

Putnam RD (1995) Bowling alone: America’s declining social capital. J Democracy 6(1):65–78CrossRef

Putnam RD (2000) Bowling alone: the collapse and revival of American Community. Simon & Schuster, New York

Satyanath S, Voigtländer N, Voth H-J (2017) Bowling for fascism: social capital and the rise of the Nazi Party. J Polit Econ 125(2):478–526CrossRef

Tabellini G (2010) Culture and institutions: economic development in the Regions of Europe. J Eur Econ Assoc 8(4):677–716CrossRef

Titel: Social Capital, Communication Channels and Opinion Formation
verfasst von: Christos Mavridis
Nikolas Tsakas
Publikationsdatum: 26.10.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 4/2021
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-020-01297-5

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